MEXICO CITY (Reuters) - Murder by firearms in Mexico have hit record levels under the government of President Enrique Pena Nieto as the death toll from gang violence worsens, a study showed on Tuesday.

The months of July to September have seen the highest murder tolls since Pena Nieto took office in December 2012 pledging to curb gang violence that rose sharply under his predecessor.

August and September, the latest months for which data are available, were also the worst two months for deaths by firearm ever registered, according to the National Citizen Observatory (ONC), a civil group monitoring justice and security in Mexico.

All told, there were 1,238 murders by firearm in August and 1,228 in September, the ONC noted, basing its findings on official data. Detailed statistics published by Mexican authorities on security stretch back to 1997.

"The main thing we want to underline is that 10 years after starting a so-called war on drugs, there's still no strategy," ONC Director Francisco Rivas told a news conference.

Almost 2,000 people were murdered in both the month of August and in September in Mexico, official data show.

Mexico has been convulsed by violence since former President Felipe Calderon sent in the armed forces to take on the drug cartels after he took office in December 2006. Well over 100,000 people have died in cartel-related violence since then.

The most violent year on record in Mexico was 2011, and this year is on track to be the worst since at least 2012.

(Reporting by Dave Graham; Editing by Lisa Shumaker)